Key Idea: Topic 4.2 is about turning raw data into visual summaries. The three key displays are: frequency distributions (grouped data tables), histograms (bars show frequency density or frequency), cumulative frequency graphs (S-curves for finding medians and quartiles), and box-and-whisker plots (five-number summaries). Each display answers a slightly different question about your data.
✅ The five-number summary and quartiles
📊 Reading cumulative frequency graphs
Example: Data: 12, 15, 18, 20, 22, 25, 30, 35 Q2 = median = (20+22)/2 = 21 Q1 = median of {12,15,18,20} = (15+18)/2 = 16.5 Q3 = median of {22,25,30,35} = (25+30)/2 = 27.5 IQR = 27.5 − 16.5 = 11 Outlier fence: below 16.5 − 16.5 = 0 or above 27.5 + 16.5 = 44 → no outliers here.
When drawing a box plot: the box spans Q1 to Q3, the line inside is Q2, and the whiskers extend to the smallest/largest non-outlier values. For grouped data: use the midpoint of each class to estimate the mean; use the upper class boundary for cumulative frequency.
Paper 2 (GDC allowed): Enter data into lists and use 1-Var Stats to get Q1, Q3, and IQR automatically. The GDC also draws box plots. Paper 1: You may be given a completed cumulative frequency graph and asked to read off the median, Q1, or Q3 — show the horizontal and vertical lines on the graph for method marks.